The Kremlin said Putin was keen to find out more about Turkey's plans. Spokesman Dmitry Peskov also said Moscow would study a "new idea" by German Defense Minister Annegret Kramp-Karrenbauer to create an internationally controlled security zone in northern Syria.
Ankara and Moscow say the talks are aimed at "normalizing the situation in Syria," where — despite supporting opposing sides — the two have indicated that they share some common ground.
Turkey, which is allied to Turkmen and Arab rebel groups in Syria, launched a cross-border offensive earlier this month against Kurdish fighters it describes as "terrorists."
Room for agreement
Russia — the strongest military backer of the Syrian state under President Bashar Assad — has traditionally opposed operations by other states in what it considers Syria's sovereign territory.
However, both sides have said they support the idea of civilian safe zones in northern Syria, and Turkey has ruffled the feathers of NATO allies by purchasing a powerful Russian anti-aircraft system, the S-400.
Despite improving relations with Ankara, Moscow has expressed concern that Turkey's incursion has helped jihadis who were in custody in Kurdish-controlled areas to escape. Russian Defense Minister Sergei Shoigu on Monday said there were concerns that battle-hardened terrorists could return to their homelands, including Russia.
Meanwhile, Assad on Tuesday vowed to reunite all of the country under the control of Damascus, and said he was ready to support any "popular resistance" against Turkey's actions. He made the comments on a visit to areas in Idlib province recently retaken by Syrian government forces from Turkey-backed rebels.